This invention is directed to measuring the characteristics of a piezoelectric element for use in a transducer and more particularly to the measurement of the piezoelectric constants (d.sub.31, d.sub.33, g.sub.31, and g.sub.33) of ceramic elements used as active elements in hydrophones and sound sources to insure quality control of the elements that made up the finished product.
The active elements of many sonar sources and hydrophones comprise one or more electrostrictive cylindrical shells. The performance of these transducers depends on the values of the piezo-electric coefficients (g.sub.31, g.sub.33, d.sub.31, d.sub.33). For a given piezo-ceramic material there is a wide variation in these constants from manufacturer to manufacturer and even from sample to sample from the same manufacturer. Currently available techniques for evaluating these coefficients either involve the use of specially prepared samples which do not have the shape of a cylindrical shell (i.e. bars, plates, disks, etc.), or involve resonance techniques which do not necessarily determine the individual piezoceramic coefficients but rather some linear combination of them in the form of an effective coupling coefficient.
It is well known tht the sensitivity of hydrophones using piezoceramic rings depends on both g.sub.31 and g.sub.33, as well as the various possible boundary conditions which may be placed on the ends of the ring.
The quantities g.sub.31 and g.sub.33 relate the electric field produced in the piezoelectric material to the applied stress. Here the 3 direction is the direction of polarization and the 1 direction is any direction perpendicular to the 3 direction. The first index indicates the electric field direction and then the second index referes to the direction of the applied stress. The quantities d.sub.31 and d.sub.33 relates the strain produced in a piezoelectric material to the applied electric field. Without previous knowledge of both g.sub.31 and g.sub.33 the sensitivity of a hydrophone could only be determined by calibration after the complete hydrophone has been assembled. When deployed in an array, precise control of individual element sensitivity is critical for minor lobe suppression. Hence, precise values for g.sub.31 and g.sub.33 are invaluable.
Often the effective coupling coefficient measured for an individual ring is not the one appropriate for the actual configuration in which the ring will be used in a transducer. For example, the effective coupling coefficient for a short, height-polarized ring measured at the first radial resonance yields essentially the k.sub.31 coupling coefficient. However, if a stack of such rings were used as the driving element of a piston source, the appropriate coupling coefficient would be essentially k.sub.33. Moreover, any mathematical model of a transducer which uses electrostrictive rings would require all piezoelectric coefficients to accurately predict all aspects of a transducer's performance.
A need, therefore, exists for a method by which d.sub.31, d.sub.33, g.sub.31, and g.sub.33 can be readily determined for a piezoceramic ring. Such a method has been set forth in a NRL Memorandum Report No. 2872 entitled Proposed Method and Device for Obtaining Piezoelectric Constants of Ceramic Cylindrical Shells, by J. F. Zalesak and P. H. Rogers, dated August 1974 and is incorporated herein as a reference.